Alternative hypothesis
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The alternative hypothesis (or maintained hypothesis or research hypothesis) and the null hypothesis are the two rival hypotheses whose likelihoods are compared by a statistical hypothesis test. Usually the alternative hypothesis is the possibility that an observed effect is genuine and the null hypothesis is the rival possibility that it has resulted from chance.
The classical (or frequentist) approach is to calculate the probability that the observed effect (or one more extreme) will occur if the null hypothesis is true. If this value (sometimes called the "p-value") is small then the result is called statistically significant and the null hypothesis is rejected in favour of the alternative hypothesis. If not, then the null hypothesis is not rejected. Incorrectly rejecting the null hypothesis is a Type I error; incorrectly failing to reject it is a Type II error.
Bayesian statisticians would challenge this approach in that it takes no account of a priori beliefs in the two hypotheses or the different consequences of taking a wrong decision; there may be good reasons (extraneous to the statistical data) for believing the null hypothesis to be correct. This must be weighed against the damning evidence of a low p-value before the null hypothesis can be rejected. Such a review often is referred to as cost-benefit analysis.
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